Improved limits on interactions of low-mass spin-0 dark matter from atomic clock spectroscopy

Low-mass (sub-eV) spin-0 dark matter particles, which form a coherently oscillating classical field $\phi = \phi_0 \cos(m_\phi t)$, can induce oscillating variations in the fundamental constants through their interactions with the Standard Model sector. We calculate the effects of such possible interactions, which may include the linear interaction of $\phi$ with the Higgs boson, on atomic and molecular transitions. Using recent atomic clock spectroscopy measurements, we derive new limits on the linear interaction of $\phi$ with the Higgs boson, as well as its quadratic interactions with the photon and light quarks. For the linear interaction of $\phi$ with the Higgs boson, our derived limits improve on existing constraints by up to $2-3$ orders of magnitude.